14A.3 Potential Vorticity As a Tool for Assessing Dynamical Impacts of Latent Heat Release in Model Forecasts

14A.3 POTENTIAL VORTICITY AS A TOOL FOR ASSESSING DYNAMICAL IMPACTS OF LATENT HEAT RELEASE IN MODEL FORECASTS

Michael J.Brennan*, Gary M. Lackmann, and Kelly M. Mahoney North Carolina State University, Raleigh, North Carolina

1. INTRODUCTION remarkable advance of NWP, several previous studies (e.g., Doswell 2004; Mass, 2003; Bosart Although the utility of potential vorticity (PV) first 2003) have noted that there is also a cost in terms of became apparent in the 1930’s, it was not until the the time available for forecasters to diagnose the landmark paper of Hoskins et al. (1985) that PV meteorological situation as they sift through an ever- principals became widely applied in atmospheric increasing volume of NWP output. In order to best research. During the re-emergence of PV in the assess the quality of available model guidance, years following the Hoskins et al. publication, forecasters need to recognize the differences in the questions regarding the utility of “PV thinking” in an guidance provided by various NWP models and operational forecasting setting naturally arose. For understand why these differences exist. This ability is example, plots of potential temperature on the hindered by the fact that it is difficult for operational dynamic tropopause (typically defined as a PV forecasters to stay abreast of changes made to the surface of value between 1 and 2 PVU1) can be models run at the National Centers for Environmental extremely useful because PV surfaces intersect the Prediction (NCEP). Therefore, it is a challenge for core of all major jet streams, even those centered at forecasters to be aware of details of the differing altitudes (Morgan and Neilsen-Gammon representation of critical physical processes in NWP 1998). models that may profoundly influence the model solution. Forecasters must also have the ability to Despite these advantages, it is our sense that PV has use observations and high-frequency model analyses yet to gain widespread acceptance by the operational to evaluate short-term model forecasts if they are to forecasting community in the U.S. There are several have the confidence necessary to make significant possible reasons for this, including (i) a lack of adjustments to model guidance in the midst of a emphasis on PV concepts in undergraduate university potentially high-impact event, which is a non-trivial curricula, (ii) a lack of training of operational task. forecasters in PV methodology, (iii) the time- consuming and technically challenging task of PV Latent heat release (LHR) is a critical physical inversion, and (iv) the failure to convincingly process, and its associated dynamical feedbacks can demonstrate that the use of PV can provide have a large impact on a wide range of information not obtainable via more traditional means. meteorological phenomena. It is widely recognized It is this last reason that we wish to address here. that quantitative precipitation forecasting (QPF) is the least accurate parameter in NWP forecasts (e.g., Rather than emphasizing upper-tropospheric Fritsch and Carbone 2004), and inaccurate QPF can representation of phenomena such as tropopause result in the misrepresentation or overprediction of folding and stratospheric PV extrusions, we will here LHR, which can introduce significant errors into the advocate a somewhat different utilization of PV synoptic-scale forecast. This is particularly true for concepts, with emphasis on PV as a means for convection, and model representation or identifying the dynamical feedbacks associated with parameterization of organized convection (e.g., Wang latent heat release and the accompanying PV non- and Seaman 1997). conservation. The goal of this study is to provide examples of situations where the application of PV Here, we advocate examination of lower-tropospheric tools can provide insight above and beyond that PV in conjunction with several other model output obtainable using traditional forecast methods. parameters that will serve to (i) alert forecasters to which synoptic or mesoscale features in the model There is no question that numerical weather output are strongly influenced by LHR, (ii) provide prediction (NWP) has become entrenched as the forecasters with a means of assessing the uncertainty most important forecasting tool for today’s operational in a particular feature in model output, (iii) allow weather forecaster. Despite verifiable improvements forecasters the opportunity to determine the sign of in forecast accuracy that have accompanied the model biases for specific features, and (iv) provide a ______conceptual and dynamical model with which * Corresponding author address: Michael J. Brennan, forecasters can understand the physical or model North Carolina State University, Dept. of Marine, processes responsible for a given feature. Most Earth and Atmospheric Sciences, Raleigh, NC importantly, through the use of PV diagnostics, 27695. E-mail: [email protected] forecasters can have an improved recognition of those situations in which they are most able to add value to a model forecast. Case study examples will 1 1 Potential Vorticity Unit (PVU) = 1.0 x 10-6 m2 s-1 K kg-1 be presented that demonstrate the utility of PV gradient of the latent heating and the magnitude of concepts in the operational forecast setting. the absolute vorticity (Stoelinga 1996).

2. BACKGROUND A second principal of PV methodology, invertibility, allows one to quantify the impact of any piece of PV on the remainder of the atmosphere by numerically Potential vorticity is the product of the absolute solving a boundary value problem assuming an vorticity and the static stability, and is defined after independent balance relationship between the wind Rossby (1940) and Ertel (1942) as: and temperature fields (Davis and Emanuel 1991). The output of the inversion includes the balanced

⎛ ∂θ ⎞ wind and geopotential height fields associated with PV = − g(ζ θ + f )⎜ ⎟ (1) the portion of the PV field inverted. It is important to ⎝ ∂p ⎠ note that balance conditions beyond geostrophy can where ηr is the absolute vorticity vector, ρ is the be employed to recover a substantial portion of the ageostrophic flow (Davis et al. 1996). density, and θ is the potential temperature. In the Northern Hemisphere high- (low-) PV air is associated Previous case studies have shown that diabatic PV with cyclonic (anticyclonic) absolute vorticity and/or maxima in the lower troposphere can impact the high (low) values of static stability (Hoskins et al. evolution of extratropical cyclones (e.g., Davis and 1985). In other words, PV maxima (minima) are Emanuel 1991; Davis 1992; Stoelinga 1996; Plant et associated with upper troughs (ridges), low (high) al. 2003). In many case the diabatic PV maximum geopotential heights and cyclonic (anti-cyclonic) flow. enhances the coupling and mutual interaction In addition, Bretherton (1966) showed that anomalies between the upper-tropospheric PV maximum and the of θ at the surface can be considered surrogate PV surface θ maximum, leading to a stronger feedback features, with warm (cold) areas of θ analogous to PV process and a more intense cyclone (e.g., Davis et al. maxima (minima). 1993; Stoelinga 1996). However, in other cases the diabatic PV maximum can hinder the interaction of the Of the two components of “PV thinking” outlined by tropopause and surface waves (Davis et al. 1992). Hoskins et al. (1985), the concept of PV conservation offers utility in operational interpretation of NWP Diabatically-generated lower-tropospheric PV maxima output by allowing unambiguous identification of can significantly impact the wind field in this layer of nonconservative processes. Since PV is conserved the atmosphere where moisture values are generally in an isentropic framework in the absence of diabatic large. This can significantly modify moisture transport processes and friction; it is not conserved in the and ultimately precipitation distribution by presence of diabatic processes, making it an ideal enhancement of the low-level jet (e.g., Whitaker et al. indicator of the impact of latent heating in the 1988; Lackmann and Gyakum 1999; Lackmann 2002; atmosphere. The feedback on atmospheric dynamics Brennan and Lackmann 2005). Additionally, from latent heating can impact cyclone evolution, low- enhanced low-level jets can result in the transport of level jets, moisture transport, and QPF, all of which high-momentum air to the surface, resulting in can be important in forecasting sensible weather in damaging wind gusts in convective or non-convective potentially high-impact events. situations.

Latent heating due to precipitation processes impacts Since most of today’s operational NWP models the PV distribution by altering the two components of continue to be run at a grid-spacing insufficient to PV, the absolute vorticity and the static stability. The resolve cumulus convection, the use of cumulus effects of LHR below the level of maximum heating parameterization (CP) schemes continues in most are to increase the static stability and hydrostatically operational NWP models. The variability in CP lower the heights, thus increasing the absolute scheme design includes how they activate or “trigger”, vorticity as the flow converges into the area of the manner in which thermodynamic adjustments are lowered heights. The increase of both the static applied, and the degree of interaction with other stability and absolute vorticity necessitates an model physics schemes (e.g., Kuo et al. 1996; increase in the PV below the level of maximum Baldwin et al. 2002; Mahoney and Lackmann 2005). heating. The opposite occurs above the level of Accordingly, there can be significant variability in if, maximum heating, resulting in a decrease in PV. when, and where different schemes activate and how Therefore, LHR associated with precipitation they re-distribute heat and moisture. Therefore, the processes generally leads to an increase (decrease) LHR from different CP schemes can significantly of PV below (above) the level of maximum heating. In impact the evolution of the PV distribution in an NWP the presence of vertical wind shear, this diabatic PV model. re-distribution is offset from vertical and occurs along the absolute vorticity vector, as discussed by Raymond (1992). The rate of PV generation or destruction is determined by the magnitude and

A B Figure 1. 700-hPa kinematic moisture flux (color shaded, g kg-1 m s-1), 700-hPa winds (barbs, kt), and 900– 700-hPa PV (red contours every 0.25 PVU above 0.5 PVU) from (a) 24-h Eta model forecast and (b) RUC model analysis valid at 00 UTC 25 January 2000.

3. CASE STUDIES direction and moisture flux of 10 g kg-1 m s-1 or less (Fig. 1a). Results from the PV inversion in Brennan a.) Moisture transport in extratropical cyclones and Lackmann (2005) showed that the lower- tropospheric PV maximum was responsible for 20–25 The East Coast cyclone of 24–25 January 2000 was a kt of this onshore flow over the eastern Carolinas, major forecast failure, as operational NWP models significantly enhancing the moisture flux into the failed to produce heavy precipitation in a region that region of heavy precipitation. received heavy snowfall from the Carolinas northward into the Washington D.C. area. Brennan and In a future case such as this where a large area of Lackmann (2005) used piecewise Ertel’s PV inversion LHR was unforecasted by the operational models, to show that a lower-tropospheric PV maximum forecasters could utilize PV methodology to recognize initially generated by latent heating associated with how an area of unforecasted latent heating could incipient precipitation (IP) over Alabama and Georgia impact the lower-tropospheric PV distribution. This early on 24 January was critical to the moisture could be confirmed by examining high-frequency transport into the region of heavy precipitation in the model analyses of the PV distribution (i.e. RUC Carolinas and Virginia. The IP was unforecasted by analyses) and lower-tropospheric wind field. Using the operational NCEP models initialized only 6–12 PV thinking, forecasters could anticipate the impact hours prior to its formation, and the absence of this that lower-tropospheric PV maxima might have on the area of substantial latent heating meant that these moisture transport and cyclone evolution and use this model forecasts were unable to generate the critical knowledge to adjust model guidance accordingly. PV maximum, and ultimately failed to capture the moisture transport into the Carolinas and Virginia later b.) Coastal cyclogenesis in the event. Previous studies have documented the influence that A comparison of the 24-h forecast of 900–700-hPa convective latent heat release can have during the layer PV from the 00 UTC 24 January 2000 Eta model cyclogenesis process (e.g., Kuo et al. 1996). It is also run (Fig. 1a) to the analysis from the RUC model at widely recognized that the prediction of convective that time (00 UTC 25 January 2000, Fig. 1b) clearly precipitation remains problematic in operational NWP shows that the Eta model did not forecast the large models, and that parameterized convection in PV maximum centered along the coast of Georgia particular can contribute to the challenge (e.g. Wang and South Carolina analyzed by the Rapid Update and Seaman 1997; Davis et al. 2003). To Cycle (RUC) model at this time. The cyclonic demonstrate how PV concepts can be used by circulation associated with this PV maximum forecasters to help them recognize features in model enhanced the onshore flow at the 700-hPa level over forecasts that are tied to the parameterization of the eastern Carolinas, where 30–35 kt of easterly flow convection in models, we present model forecasts generates moisture flux values of 50–100 g kg-1 m s-1 and PV diagnostics from the coastal cyclone event of in this region (Fig. 1b). In contrast, the Eta forecast 17 February 2004 (see Mahoney and Lackmann 2005 without the PV maximum along the coast shows only for additional details). 5 kt or less of wind in this region with a variable

a. b.

Figure 2. (a) Workstation Eta forecast of 900–700 hPa potential vorticity (PVU (1 PVU = 10-6 m3 s-1 K kg-1), shaded as in legend at left of panel), SLP (hPa, dashed contours), and 3-h convective precipitation forecast (mm, red solid contours) valid 21 UTC 17 Feb. using (a) BMJ CP scheme and (b) KF CP scheme.

During the 17 February 2004 event, a strong upper- c.) Low-level jet level trough moved eastward across the southeastern US, while at the same time an Appalachian cold-air Low-level jets can be important to moisture transport damming (CAD) event was underway (not shown). and the transport of high-momentum air to the As the upper trough approached a coastal front that surface, which can result in wind damage at the was located to the east of the CAD event, surface in both convective and non-convective cyclogenesis ensued, both in model forecasts and in events. To demonstrate how forecasters can the real atmosphere. Operational forecasters, as well recognize the enhancement of a low-level jet by latent as the authors, recognized that local maxima of heat release through PV concepts, we present an convective precipitation were collocated with the event from 1 December 2004 that resulted in formative surface cyclone centers (Fig. 2a). Given widespread wind damage in 15 states from the mid- the inherent uncertainty of parameterized convection, Atlantic into New England, resulting in more than $1.5 these features were viewed with somewhat less million of property damage, two fatalities, and five confidence than other features of the model forecast. injuries (NCDC 2005).

In order to examine the sensitivity of the cyclogenesis At 12 UTC 1 December 2004, a surface cyclone was to the choice of CP scheme, Mahoney and Lackmann located in western New York State with a surface (2005) re-ran the Workstation Eta model forecast with warm front extending eastward to northern New all conditions identical except for use of the Kain- England and a surface cold front extending south into Fritsch (KF) CP scheme in place of the Betts-Miller- the central Carolinas (not shown). A prominent band Janjic (BMJ) scheme. The resulting forecast (Fig. 2b) of precipitation was seen in radar imagery along and confirms that the character of the coastal cyclone in ahead of the cold front over the Mid-Atlantic states at this case was extremely sensitivity to convective 09 UTC (Fig. 3). Through the period from 09–12 UTC parameterization. a 900–700-hPa PV maximum formed in the wake of this precipitation ahead of the advancing cold front, By plotting the lower-tropospheric PV along with the reaching a magnitude of 1.25 PVU by 12 UTC in the convective precipitation forecast and sea level RUC analysis (Fig. 4). pressure, one can easily identify features that are tied to CP scheme activity. While the purpose is not to A low-level jet was seen at the 850-hPa level east of demonstrate the superiority of one CP scheme over the PV maximum where wind speeds increase to another, it is clear that by the use of PV diagnostics to more than 70 kt from central Virginia to eastern identify lower-tropospheric diabatic PV maxima that Pennsylvania (Fig 4b). By 15 UTC the low-level jet are generated by the parameterized convective continued to intensify to the east of the PV maximum activity, one can more easily assess the forecast reaching into New York and southern New England confidence in these features. (not shown).

Figure 3. Radar mosaic imagery valid at 09 UTC 1 December 2004.

A B Figure 4. RUC analysis of 900–700-hPa PV (color shaded every 0.25 PVU starting at 1.00 PVU), 850-hPa wind (barbs, kt), and 850-hPa isotachs (red contours every 10 kt starting at 50 kt) valid at (a) 09 UTC and (b) 12 UTC 1 December 2004.

By overlaying model analyses of lower-tropospheric lower-tropospheric PV maxima represents a more PV, winds, and radar imagery, forecasters can identify compelling motive for operational forecasters to situations when a lower-tropospheric PV maximum embrace PV concepts, as fewer alternatives exist that associated with latent heating is enhancing the allow forecasters to assess the dynamical impact of intensity of a low-level jet. By comparing model often highly uncertain diabatic processes in a model forecasts of precipitation, the PV distribution and wind forecast. speed to analyses, forecasters may be able to recognize situations when the model forecast of the The conservation property of PV allows a generally jet may be degraded due to misrepresenting or reliable method for (i) identifying those lower- underforecasting LHR. tropospheric features that are driven strongly by model latent heat release, and (ii) obtaining a ready 4. DISCUSSION estimation of the dynamical impact that these features may have on the forecast evolution. Bearing in mind Although there are documented advantages to using the uncertainty inherent in model QPF, particularly tropopause maps and plots of isentropic PV as a that due to parameterized precipitation, the use of PV means of diagnosing upper-tropospheric dynamics, it in this manner provides forecasters with a tool that can be argued that alternate techniques can provide can be used in conjunction with ensemble forecasts to forecasters with much of the same information. yield a sense of forecast confidence in given features However, here we argue that the use of PV as a of a model forecast. means to identify and diagnose diabatically produced We advocate plotting of lower-tropospheric (e.g., Fritsch, J. M.,and R. E. Carbone, 2004: Improving 900–700 hPa) PV and winds, with convective and/or quantitative precipitation forecasts in the warm total precipitation superimposed in order to provide a season: A USWRP research and development generally reliable indicator of those PV features strategy. Bull Amer. Meteor. Soc., 85, 955–965. associated with model-generated latent heat release. Additional research, fine-tuning of graphical displays, Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, and training modules could serve to help this 1985: On the use and significance of isentropic forecasting tool gain a deserved acceptance in the potential vorticity maps. Quart. J. Roy. Meteor. Soc., operational forecasting community in general. 111, 877−946.

5. ACKNOWLEDGEMENTS Kuo, Y.-H., R. J. Reed, and Y. Liu, 1996: The ERICA IOP 5 storm. Part III: Mesoscale cyclogenesis and Support for this research was provided by NOAA precipitation parameterization. Mon. Wea. Rev., 124, Collaborative Science, Technology, and Applied 1409−1434. Research (CSTAR) Grant NA03NWS4680007 and NA-07WA0206, and NSF Grant ATM-0342691, all Lackmann, G. M., 2002: Cold-frontal potential vorticity awarded to North Carolina State University. Kermit maxima, the low-level jet, and moisture transport in Keeter, Jonathan Blaes, and other forecasters at the extratropical cyclones. Mon. Wea. Rev., 130, 59−74. Raleigh National Weather Service office are ⎯⎯⎯, and J. G. Gyakum, 1999: Heavy cold-season acknowledged for their encouragement and technical precipitation in the northwestern United States: assistance. Mosaic radar imagery was obtained from Synoptic climatology and an analysis of the flood of NCDC. 17−18 January 1986. Wea. Forecasting, 14, 6. REFERENCES 687−700.

Baldwin, M. E., J. S. Kain, and M. P. Kay, 2002: Mahoney, K. M., and G. M. Lackmann, 2005: The Properties of the convection scheme in NCEP's Eta sensitivity of numerical forecasts to convective model that affect forecast sounding interpretation. parameterization: A case study of the 17 February Wea. Forecasting, 17, 1063–1079. 2004 east coast cyclone. Submitted to Wea. Forecasting. Bosart, L. F., 2003: Wither the weather analysis and forecasting process? Wea. Forecating, 18, 520–529. Mass, C. F., 2003: IFPS and the future of the National Weather Service. Wea. Forecasting, 18, 75–79. Brennan, M. J., and G. M. Lackmann, 2005: The influence of incipient latent heat release on the Morgan, M. C., and J. W. Nielsen-Gammon, 1998: precipitation distribution of the 24−25 January 2000 Using tropopause maps to diagnose midlatitude East Coast cyclone. Mon. Wea. Rev., 133, 1913– weather systems. Mon. Wea. Rev., 126, 2555−2579. 1937. NCDC, cited 2005: U.S. local storm events data. Bretherton, F. P., 1966: Critical layer instability in [Available online at http://www4.ncdc.noaa.gov/cgi- baroclinic flows. Quart. J. Roy. Meteor. Soc., 92, win/wwcgi.dll?wwEvent~Storms] 325−334. Plant, R. S., G. C. Craig, and S. L. Gray, 2003: On a Davis, C. A., 1992: A potential-vorticity diagnosis of threefold classification of extratropical cyclogenesis. the importance of initial structure and condensational Quart. J. Roy. Meteor. Soc., 129, 2989−3012. heating in observed extratropical cyclogenesis. Mon. Raymond, D. J., 1992: Nonlinear balance and Wea. Rev., 120, 2409−2428. potential-vorticity thinking at large Rossby number. ⎯⎯⎯, and K. A. Emanuel, 1991: Potential vorticity Quart. J. Roy. Meteor. Soc., 118, 987−1015. diagnostics of cyclogenesis. Mon. Wea. Rev., 119, Rossby, C.-G., 1940: Planetary flow patterns in the 1929−1953. atmosphere. Quart. J. Roy. Meteor. Soc., 66, Supl., ⎯⎯⎯, M. T. Stoelinga, and Y.-H. Kuo, 1993: The 68−87. integrated effect of condensation in numerical Stoelinga, M. T., 1996: A potential-vorticity based simulations of extratropical cyclogenesis. Mon. Wea. study of the role of diabatic heating and friction in a Rev., 121, 2309−2330. numerically simulated baroclinic cyclone. Mon. Wea. ⎯⎯⎯, E. D. Grell, and M. A. Shapiro, 1996: The Rev., 124, 849−874. balanced dynamical nature of a rapidly intensifying Wang, W., N. L. Seaman, 1997: A comparison study oceanic cyclone. Mon. Wea. Rev., 124, 3–26. of convective parameterization schemes in a Doswell, C. A., 2004: Weather forecasting by mesoscale model. Mon. Wea. Rev., 125, 252–278. humans—heuristics and decision making. Wea. Whitaker, J. S., L. W. Uccellini, and K. F. Brill, 1988: A Forecasting, 19, 1115–1126. model-based diagnostic study of the rapid Ertel, H., 1942: Ein Neuer hydrodynamischer development phase of the Presidents’ Day cyclone. Wirbelsatz. Meteor. Zeits., 59, 271−281. Mon. Wea. Rev., 116, 2337–2365.